From our analysis it appears that the large deviation limit per se
can not be used to characterize heat waves: due to the presence of
the seasonal cycle in the real world, heat waves are of interest up
to time period of a season, about 90 days, that as we have seen is
far from the time scales for which the large deviation rate function
gives meaningful informations. In a recent paper, [1]}
performed a large deviation analysis of surface temperatures using
the model Puma, which consists in the dynamical core of Plasim, obtaining
faster convergence rates than what we observe. Puma is essentially
Plasim without physical parameterizations, which are substituted by
Newtonian cooling. As a consequence the dynamics in Puma does not
include the range of processes which determine the surface fluxes
of sensible and latent heat, and that lead to memory effects on time
scales longer than the synoptic scale. The faster convergence rates
is very probably due to this aspect. In more realistic setups, from
our analysis it seems unlikely that the statistics of the surface
temperature averaged at regional scale could converge to the large
deviation limit on time scales shorter that a few years, which makes
it not directly relevant for applications.
